Mean temperament in the music of Bach, I think, was discussed in the old GMG. It might be well to bring the subject up again as it is a terribly important issue. I was really astonished by the revelations of this article and website:
http://bach.tuning.googlepages.com/introductionThe number of spirals in the heading of the WTC, handwritten by Bach, referred to the beats of a mean or rather "well" tempered keyboard:
"Tuning is performed for some twelve semitone contiguous range.
The small knot is the basic tempering unit, which denotes one beat per second, while the double knot indicates two beats per second (or equivalently one beat per second in the octave below).
The ends of the spiral denote the interval closing the tuning circle and two cases are shown beating once per second (left) and twice per second (right)."
There's some incredible stuff here too:
http://www.uk-piano.org/edfoote/well_tempered_piano.html"Debated for thousands of years, temperament is an arcane subject to most musicians today. This may be due to 20th century use of Equal Temperament. With equal harmony and dissonance everywhere in the scale, there is little to debate about different keys' characters. As a result, most modern ears have become accustomed to an ever-present, mild dissonance in keyboard harmony, never hearing a harsh third or a pure one, either."
This has to do mainly with the tuning of thirds as I understand it. In certain keys like C, the major thirds in "well" tuning are pure, or free of beats. Hearing or playing the WTC according to Bach's tuning must be a revelation. This of course would contradict what Schoenberg had to say about tonality, since everything is transposable, all tonal music is in the key of C.
Interest in this must be fairly recent (although I ALWAYS had questions about it while studying). Grout dismisses the tuning of Bach in one sentence, saying that he probably preferred equal temperament (although this was not the most popular then). Even Badura-Skoda's book about the Interpretation
of Bach at the Keyboard (1990) says virtually nothing about the differing systems of tuning.
Any comments? I find this subject REALLY exciting.
ZB